In her inaugural lecture Jun.Prof. Carina Bringedal, PhD., will talk in the course of the SimTech colloquium about Evolving Interfaces in Porous Media.
Porous media have highly oscillatory characteristics, with rapid micro-scale changes between the solid matrix and the fluid-filled void space. If simulating the micro-scale flow, very detailed domains and fine grids are needed. Usually, when modeling flow and transport through a porous medium, only the averaged behavior is sought and a macro-scale approach is used. In this case, the flow rate depends on the permeability of the porous medium and being able to determine the value of the permeability becomes essential. Through analytical upscaling using homogenization and asymptotic expansions, expressions for the permeability can (under certain assumptions) be found.
Things get more complicated (and more interesting) when there are evolving interfaces involved; that is, either a solid-fluid interface due to a chemical reaction or a fluid-fluid interface due to the porous medium being filled by two immiscible fluids. Then, determining the permeability and other effective properties is not straightforward. In this talk we go through how to mathematically model these evolving interfaces and how to incorporate them in the homogenization. Also, we dig into how to solve the resulting upscaled models numerically.